A wave theory for the negative mass instability

Charged particle beam transport has been recently described in terms of a quantum-like model, called Thermal Wave Model (TWM). Within the framework of TWM, the longitudinal dynamics of a relativistic charged particle beam in an accelerating machine is presented. It is shown that this dynamics is governed by a nonlinear Schrodinger-like equation for a complex function (the beam wave function) whose squared modulus is proportional to the beam number density. This way it is shown that such a description provides a wave theory for negative mass instability which is fully similar to the one used for describing oscillating two stream instability in plasma physics.